Stability and Neimark—Sacker bifurcation analysis of a food-limited population model with a time delay
Stability and Neimark—Sacker bifurcation analysis of a food-limited population model with a time delay
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DOI：
10.1088/1674-1056/22/3/030204
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发表时间：
2013-03
影响因子：
1.7
通讯作者：
Xiao-Wei 晓伟 Jiang 姜;Z. Guan 关;Xian-He 先鹤 Zhang 张;Ding-Xue 顶学 Zhang 张;F. Liu 刘
中科院分区：
文献类型：
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作者：
Xiao-Wei 晓伟 Jiang 姜;Z. Guan 关;Xian-He 先鹤 Zhang 张;Ding-Xue 顶学 Zhang 张;F. Liu 刘
本文研究了一类离散时滞食物限制模型，其中离散时滞τ为参数，利用欧拉方法得到了该模型.通过分析相应的特征方程，研究了该模型的线性稳定性。结果表明，当τ超过某个临界值时，出现Neimark-Sacker分岔。利用中心流形和规范形理论，导出了确定分支周期解的稳定性、方向性等性质的显式公式。最后，数值模拟进行验证分析结果。
In this paper, a kind of discrete delay food-limited model obtained by the Euler method is investigated, where the discrete delay τ is regarded as a parameter. By analyzing the associated characteristic equation, the linear stability of this model is studied. It is shown that Neimark—Sacker bifurcation occurs when τ crosses certain critical values. The explicit formulae which determine the stability, direction, and other properties of bifurcating periodic solution are derived by means of the theory of center manifold and normal form. Finally, numerical simulations are performed to verify the analytical results.